KnowledgeBoat Logo
|

Mathematics

Assertion: The product of two proper fractions is less than each of the fractions.

Reason: For any two fractions ab\dfrac{a}{b} and cb\dfrac{c}{b}, we have, ab×cb=acb\dfrac{a}{b} \times \dfrac{c}{b} = \dfrac{ac}{b}.

  1. Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).
  2. Both Assertion (A) and Reason (R) are true but Reason (R) is not the correct explanation of Assertion (A).
  3. Assertion (A) is true but Reason (R) is false.
  4. Assertion (A) is false but Reason (R) is true.

Fractions

2 Likes

Answer

Assertion (A) is true but Reason (R) is false.

Explanation

A proper fraction is less than 1.

When we multiply two numbers less than 1, the result becomes even smaller.

Example:

12×13=16\dfrac{1}{2} \times \dfrac{1}{3} = \dfrac{1}{6}

16\dfrac{1}{6} is smaller than both 12\dfrac{1}{2} and 13\dfrac{1}{3}

So, the Assertion is true.

The given formula in the Reason is incorrect.
Correct multiplication rule is:

ab×cb=acbd\dfrac{a}{b} \times \dfrac{c}{b} = \dfrac{ac}{bd}

But the reason states the denominator remains b, which is wrong.

So, the Reason is false.

Hence, option 3 is the correct option.

Answered By

1 Like

Related Questions